Extracted Text

The following text was automatically extracted from the image on this page using optical character recognition software:

APPENDIX BDISCUSSION OF THE REFERENCE FLUTTER SPEED

For use in comparing data of swept and unswept wings, areference flutter speed V1 is convenient. This referenceflutter speed is the flutter speed determined from the simpli-fied theory of reference 7. This theory deals with tNwo-dimensional unswept wings in incompressible flow and de-pends upon a number of wing parameters. The calculationsin this report utilize parameters of sections perpendicular tot le leading edge, first bending frequency, uncoupled torsionfrequency, density of testing medium at time of flutter, andzero damping. Symbolically,VR=bwcf(KXcxieatrc 2 )Variation in reference flutter speed with sweep angle forsheared swept wings.-The reference flutter speed isindependent of sweep angle for a homogeneous rotated wingand for homogeneous wings swept back by keeping the length-chord ratio constant. For a series of homogeneous wingsswept back by the method of shearing, however, a definitevariation in reference flutter speed with sweep angle existssince sweeping a wing by shearing causes a reduction inchord perpendicular to the wing leading edge and an increasein length along the midchord as the angle of sweep is in-creased. The resulting reduction in the mass-density-ratioparameter and first bending frequency tends to raise thereference flutter speed, whereas the reduction in semichordtends to lower the reference flutter speed as the angle ofsweep is increased. The final effect upon the referenceflutter speed depends on the other properties of the wing.The purpose of this section is to show the effect of thesechanges on the magnitude of the reference flutter speed fora series of homogeneous sheared wings having propertiessimilar to those of the sheared swept models used in thiisreport.Let the subscript 0 refer to properties of the wing at zerosweep angle. The following parameters are then functionsof the sweep angle:b=bo cos Acos A248

Since m is proportional to b,brp 2K= -= K cos ASinfilarly, since I is proportional to b,0.56 I,f, =--v- = (a)o(cos A)2Also, because f, is independent of A,h (cos A)'An estimate of the effect on the flutter speed of thesechanges in semichord and mass parameter with sweep anglemay be obtained from the approximate formula given inreference 7,V r, 0.5VE - i 0.5+a+xm -=8 os AThis approximate analysis of the effect on the referenceflutter speed does not depend upon the first bending frequencybut assumesfh/f. to be small.In order to include the effect of changes in bending-torsionfrequency ratio, a more complete analysis must be carriedout. Figure 20 presents some results of a numerical analysisbased on a homogeneous wing with properties at zero sweepangle as. follows:

x.,=50x,.= 45r '- 0.25f,= 100

bo=0.333(D= 10( -=0.4

In figure 20 the curve showing the decrease in V, with A isslightly above the /cos A factor indicated by the approxi-mate formula.Effect of elastic-axis position on reference flutter speed.-As pointed out in the definition of elastic axis, the measured